Consumer demand for rail transportation has traditionally been analyzed by means of aggregate demand systems and disaggregate discrete choice models. It is remarkable however that no serious efforts have been made to develop a disaggregate structural demand model, which takes account of the fact that consumers face a nonlinear budget constraint. It is argued that the use of such a model is necessary, because individuals typically have the opportunity to choose between many different types of tickets. It is therefore clear that consumer demand for transportation not only depends on price, but also that the 'consumption' of a certain amount of transportation will have causal influence on price. An important distinction between the present case and earlier studies of 'discrete/continuous goods', such as labor supply and electricity demand, concerns the nature of the discrete choice: While in earlier applications one single simultaneous choice is made for both the discrete and the continuous choice, the demand for transportation requires two explicit choices - a discrete choice for mode and/or ticket type and a continuous choice for the amount of transportation. Evidence from our data suggests that the explicit nature of the discrete choice is likely to lead to an extra source of optimization error as compared to Hausman's 1985 overview, which means that many observed combinations of discrete and continuous choice are demonstrably suboptimal - regardless of individual preferences. Estimation of the model for non-peak hour travelers by train in the Netherlands shows that the (absolute value of the) price elasticity of the demand for train kilometers equals about unity, and that the income elasticity is fairly small (about 0.05). It is suggested that the estimated model can be extended in many ways.